arXiv subjects

Gergely Flamich

Publications and source records attributed to Gergely Flamich.

At least 19 recordsLinked to original sources

arXiv2026

Scalable Differentially Private Data Compression via Diffusion and Stochastic Codes

The ever-increasing collection of personal data has created mounting pressure to develop technologies that protect sensitive aspects of individual identity. Differential privacy (DP) provides a principled framework with strong formal guarantees and has already achieved practical success. However, releasing high-dimensional data, such as images, has remained elusive: releasing uncompressed privatized data requires significant storage. At the same time, no effective data compression scheme exists that can compress high-resolution data with privacy guarantees. We address this challenge with DP-DiPP, a compression pipeline that combines stochastic codes with diffusion models. DP-DiPP is highly flexible: the practitioner has direct control over the compression rate-privacy-utility tradeoff. As the theoretical backbone, we extend the Poisson private representation (PPR) to encode the outputs of privacy mechanisms. We then combine it with DiffC, a diffusion-based lossy data compression method, to obtain a differentially private image compressor. Our experiments on privatized image classification on CIFAR-10 demonstrate that DP-DiPP significantly outperforms the baseline, achieving a 10-30 times better compression while retaining comparable privacy guarantees and utility.

cs.CR↗

arXiv2026

Multi-Marginal Couplings for Metropolis-Hastings

Convergence diagnosis for Markov chain Monte Carlo is a matter of fundamental importance in computational statistics: it determines the resources allocated to a particular sampling problem and influences the practitioner's view of the quality of estimates obtained from a Markov chain. Motivated by this, we contribute to the emerging class of coupling-based convergence diagnostic algorithms. Concretely, we study coupling multiple Metropolis-Hastings chains using multi-marginal coupling. We introduce a natural objective for this setting and establish lower and upper bounds by drawing connections to list-level distribution coupling and distributed pairwise-matching problems. This analysis ultimately leads to a shared-randomness Poisson Monte Carlo construction for coupling multiple Markov chains. In this process, we avoid a key dimension-dependent bottleneck in the runtime complexity of classical Poisson Monte Carlo by developing an adaptive rule for updating the point process, yielding significant gains in high-dimensional settings. Experiments on grand couplings of Markov chains show that our methods improve coalescence rates across dimensions, reducing meeting times by up to 50% compared with existing baselines.

stat.CO↗

arXiv2026

Rejection Sampling is Optimal for Relative Entropy Coding

In relative entropy coding, a sender aims to design a stochastic code such that, on input $X \sim P_X$, the receiver can generate a sample $Y \sim P_{Y \mid X}$. It is a standard result that (1) this requires at least $I(X; Y)$ bits, (2) the lower bound is achievable within a logarithmic gap, and (3) this gap cannot be reduced in general. The necessity of the gap suggests that the mutual information is not the correct information measure to quantify the rate of relative entropy coding. A potential alternative emerged in the work of Flamich et al. (2025), who proved a tighter lower bound of $I_F(X \to Y)$, a quantity we call the functional information. In this paper, we construct the ring toss code, an encoding method for rejection sampling which uses at most $I_F(X \to Y) + \log e$ bits, hence obtaining a tight one-shot characterization of relative entropy coding. For the trivial channel $Y = X$, our result recovers the noiseless source coding theorem within a small constant. For a general channel, it implies that the classical mutual information lower bound is achievable within $\log(I(X; Y) + 1) + 2.45$ bits in general and within $1.45$ bits for singular channels, which are both the tightest bounds of their kind to date. Moreover, our one-shot result also recovers Sriramu and Wagner's asymptotic results on the second-order redundancy of relative entropy codes.

cs.IT↗

arXiv2026

Singular Relative Entropy Coding with Bits-Back Rejection Sampling

A relative entropy code for a source $X \sim P_X$ is a stochastic code that encodes random samples from a prescribed $P_{Y \mid X}$ using as few bits as possible. A generalisation of entropy coding, it is a standard result that the minimum number of bits required to achieve this is at least the mutual information $I[X\,\Vert\,Y]$. However, a particularly fascinating feature of relative entropy coding compared to entropy coding is that, in general, this lower bound is only achievable to within an additional logarithmic factor. As such, an important research direction is to identify channels where we can reduce this gap. Sriramu and Wagner achieved such success by exhibiting a relative entropy code for so-called singular channels with sub-logarithmic asymptotic redundancy. However, their code is quite involved and, sadly, cannot be implemented in practice. In this paper, we construct the bits-back rejection sampler (BBRS), a relative entropy code that combines ideas from bits-back coding and (greedy) rejection sampling. Our analysis of BBRS reveals that the algorithm achieves the same asymptotic efficiency as Sriramu and Wagner's sampler, but with much simpler analysis and better constants. Moreover, BBRS can be implemented using standard relative entropy coding methods.

cs.IT↗

arXiv2026

Data Compression with Stochastic Codes

Machine learning has had a major impact on data compression over the last decade and opened up many new theoretical and applied fields of inquiry. This paper describes one such direction -- relative entropy coding -- which focuses on constructing stochastic codes, mainly as an alternative to quantisation and entropy coding in lossy source coding. Our primary aim is to provide a broad overview of the topic, with an emphasis on the computational and practical aspects currently missing from the literature. Our goal is threefold: for the curious reader, we aim to provide an intuitive picture of the field and convince them that relative entropy coding is a simple yet exciting emerging field in data compression research. For a reader interested in applied research on lossy data compression, we provide an account of the most salient contemporary applications. Finally, for the reader who has heard of relative entropy coding but has never been quite sure what it is or how the algorithms fit together, we hope to illustrate how simple and elegant the underlying constructions are.

cs.IT↗

arXiv2025

Data Compression with Relative Entropy Coding

Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio recordings of animals) or users' audiovisual perception. This, in turn, has led to an explosion of theoretical investigations and insights that aim to develop new fundamental theories, methods and algorithms better suited for machine learning-based compressors. In this thesis, I contribute to this trend by investigating relative entropy coding, a mathematical framework that generalises classical source coding theory. Concretely, relative entropy coding deals with the efficient communication of uncertain or randomised information. One of its key advantages is that it extends compression methods to continuous spaces and can thus be integrated more seamlessly into modern machine learning pipelines than classical quantisation-based approaches. Furthermore, it is a natural foundation for developing advanced compression methods that are privacy-preserving or account for the perceptual quality of the reconstructed data. The thesis considers relative entropy coding at three conceptual levels: After introducing the basics of the framework, (1) I prove results that provide new, maximally tight fundamental limits to the communication and computational efficiency of relative entropy coding; (2) I use the theory of Poisson point processes to develop and analyse new relative entropy coding algorithms, whose performance attains the theoretic optima and (3) I showcase the strong practical performance of relative entropy coding by applying it to image, audio, video and protein data compression using small, energy-efficient, probabilistic neural networks called Bayesian implicit neural representations.

cs.IT↗

arXiv2025

You Cannot Feed Two Birds with One Score: the Accuracy-Naturalness Tradeoff in Translation

The goal of translation, be it by human or by machine, is, given some text in a source language, to produce text in a target language that simultaneously 1) preserves the meaning of the source text and 2) achieves natural expression in the target language. However, researchers in the machine translation community usually assess translations using a single score intended to capture semantic accuracy and the naturalness of the output simultaneously. In this paper, we build on recent advances in information theory to mathematically prove and empirically demonstrate that such single-score summaries do not and cannot give the complete picture of a system's true performance. Concretely, we prove that a tradeoff exists between accuracy and naturalness and demonstrate it by evaluating the submissions to the WMT24 shared task. Our findings help explain well-known empirical phenomena, such as the observation that optimizing translation systems for a specific accuracy metric (like BLEU) initially improves the system's naturalness, while ``overfitting'' the system to the metric can significantly degrade its naturalness. Thus, we advocate for a change in how translations are evaluated: rather than comparing systems using a single number, they should be compared on an accuracy-naturalness plane.

cs.CL↗

arXiv2025

The Redundancy of Non-Singular Channel Simulation

Channel simulation is an alternative to quantization and entropy coding for performing lossy source coding. Recently, channel simulation has gained significant traction in both the machine learning and information theory communities, as it integrates better with machine learning-based data compression algorithms and has better rate-distortion-perception properties than quantization. As the practical importance of channel simulation increases, it is vital to understand its fundamental limitations. Recently, Sriramu and Wagner provided an almost complete characterisation of the redundancy of channel simulation algorithms. In this paper, we complete this characterisation. First, we significantly extend a result of Li and El Gamal, and show that the redundancy of any instance of a channel simulation problem is lower bounded by the channel simulation divergence. Second, we give two proofs that the asymptotic redundancy of simulating iid non-singular channels is lower-bounded by $1/2$: one using a direct approach based on the asymptotic expansion of the channel simulation divergence and one using large deviations theory.

cs.IT↗

arXiv2024

Getting Free Bits Back from Rotational Symmetries in LLMs

Current methods for compressing neural network weights, such as decomposition, pruning, quantization, and channel simulation, often overlook the inherent symmetries within these networks and thus waste bits on encoding redundant information. In this paper, we propose a format based on bits-back coding for storing rotationally symmetric Transformer weights more efficiently than the usual array layout at the same floating-point precision. We evaluate our method on Large Language Models (LLMs) pruned by SliceGPT (Ashkboos et al., 2024) and achieve a 3-5% reduction in total bit usage for free across different model sizes and architectures without impacting model performance within a certain numerical precision.

cs.IT↗

arXiv2024

Accelerating Relative Entropy Coding with Space Partitioning

Relative entropy coding (REC) algorithms encode a random sample following a target distribution $Q$, using a coding distribution $P$ shared between the sender and receiver. Sadly, general REC algorithms suffer from prohibitive encoding times, at least on the order of $2^{D_{\text{KL}}[Q||P]}$, and faster algorithms are limited to very specific settings. This work addresses this issue by introducing a REC scheme utilizing space partitioning to reduce runtime in practical scenarios. We provide theoretical analyses of our method and demonstrate its effectiveness with both toy examples and practical applications. Notably, our method successfully handles REC tasks with $D_{\text{KL}}[Q||P]$ about three times greater than what previous methods can manage, and reduces the bitrate by approximately 5-15% in VAE-based lossless compression on MNIST and INR-based lossy compression on CIFAR-10, compared to previous methods, significantly improving the practicality of REC for neural compression.

cs.IT↗

arXiv2024

Some Notes on the Sample Complexity of Approximate Channel Simulation

Channel simulation algorithms can efficiently encode random samples from a prescribed target distribution $Q$ and find applications in machine learning-based lossy data compression. However, algorithms that encode exact samples usually have random runtime, limiting their applicability when a consistent encoding time is desirable. Thus, this paper considers approximate schemes with a fixed runtime instead. First, we strengthen a result of Agustsson and Theis and show that there is a class of pairs of target distribution $Q$ and coding distribution $P$, for which the runtime of any approximate scheme scales at least super-polynomially in $D_\infty[Q \Vert P]$. We then show, by contrast, that if we have access to an unnormalised Radon-Nikodym derivative $r \propto dQ/dP$ and knowledge of $D_{KL}[Q \Vert P]$, we can exploit global-bound, depth-limited A* coding to ensure $\mathrm{TV}[Q \Vert P] \leq ε$ and maintain optimal coding performance with a sample complexity of only $\exp_2\big((D_{KL}[Q \Vert P] + o(1)) \big/ ε\big)$.

cs.IT↗

arXiv2024

On Channel Simulation with Causal Rejection Samplers

One-shot channel simulation has recently emerged as a promising alternative to quantization and entropy coding in machine-learning-based lossy data compression schemes. However, while there are several potential applications of channel simulation - lossy compression with realism constraints or differential privacy, to name a few - little is known about its fundamental limitations. In this paper, we restrict our attention to a subclass of channel simulation protocols called causal rejection samplers (CRS), establish new, tighter lower bounds on their expected runtime and codelength, and demonstrate the bounds' achievability. Concretely, for an arbitrary CRS, let $Q$ and $P$ denote a target and proposal distribution supplied as input, and let $K$ be the number of samples examined by the algorithm. We show that the expected runtime $\mathbb{E}[K]$ of any CRS scales at least as $\exp_2(D_\infty[Q || P])$, where $D_\infty[Q || P]$ is the Rényi $\infty$-divergence. Regarding the codelength, we show that $D_{KL}[Q || P] \leq D_{CS}[Q || P] \leq \mathbb{H}[K]$, where $D_{CS}[Q || P]$ is a new quantity we call the channel simulation divergence. Furthermore, we prove that our new lower bound, unlike the $D_{KL}[Q || P]$ lower bound, is achievable tightly, i.e. there is a CRS such that $\mathbb{H}[K] \leq D_{CS}[Q || P] + \log_2 (e + 1)$. Finally, we conduct numerical studies of the asymptotic scaling of the codelength of Gaussian and Laplace channel simulation algorithms.

cs.IT↗

arXiv2024

Greedy Poisson Rejection Sampling

One-shot channel simulation is a fundamental data compression problem concerned with encoding a single sample from a target distribution $Q$ using a coding distribution $P$ using as few bits as possible on average. Algorithms that solve this problem find applications in neural data compression and differential privacy and can serve as a more efficient alternative to quantization-based methods. Sadly, existing solutions are too slow or have limited applicability, preventing widespread adoption. In this paper, we conclusively solve one-shot channel simulation for one-dimensional problems where the target-proposal density ratio is unimodal by describing an algorithm with optimal runtime. We achieve this by constructing a rejection sampling procedure equivalent to greedily searching over the points of a Poisson process. Hence, we call our algorithm greedy Poisson rejection sampling (GPRS) and analyze the correctness and time complexity of several of its variants. Finally, we empirically verify our theorems, demonstrating that GPRS significantly outperforms the current state-of-the-art method, A* coding. Our code is available at https://github.com/gergely-flamich/greedy-poisson-rejection-sampling.

cs.IT↗

arXiv2024

RECOMBINER: Robust and Enhanced Compression with Bayesian Implicit Neural Representations

COMpression with Bayesian Implicit NEural Representations (COMBINER) is a recent data compression method that addresses a key inefficiency of previous Implicit Neural Representation (INR)-based approaches: it avoids quantization and enables direct optimization of the rate-distortion performance. However, COMBINER still has significant limitations: 1) it uses factorized priors and posterior approximations that lack flexibility; 2) it cannot effectively adapt to local deviations from global patterns in the data; and 3) its performance can be susceptible to modeling choices and the variational parameters' initializations. Our proposed method, Robust and Enhanced COMBINER (RECOMBINER), addresses these issues by 1) enriching the variational approximation while retaining a low computational cost via a linear reparameterization of the INR weights, 2) augmenting our INRs with learnable positional encodings that enable them to adapt to local details and 3) splitting high-resolution data into patches to increase robustness and utilizing expressive hierarchical priors to capture dependency across patches. We conduct extensive experiments across several data modalities, showcasing that RECOMBINER achieves competitive results with the best INR-based methods and even outperforms autoencoder-based codecs on low-resolution images at low bitrates. Our PyTorch implementation is available at https://github.com/cambridge-mlg/RECOMBINER/.

cs.LG↗

arXiv2023

Minimal Random Code Learning with Mean-KL Parameterization

This paper studies the qualitative behavior and robustness of two variants of Minimal Random Code Learning (MIRACLE) used to compress variational Bayesian neural networks. MIRACLE implements a powerful, conditionally Gaussian variational approximation for the weight posterior $Q_{\mathbf{w}}$ and uses relative entropy coding to compress a weight sample from the posterior using a Gaussian coding distribution $P_{\mathbf{w}}$. To achieve the desired compression rate, $D_{\mathrm{KL}}[Q_{\mathbf{w}} \Vert P_{\mathbf{w}}]$ must be constrained, which requires a computationally expensive annealing procedure under the conventional mean-variance (Mean-Var) parameterization for $Q_{\mathbf{w}}$. Instead, we parameterize $Q_{\mathbf{w}}$ by its mean and KL divergence from $P_{\mathbf{w}}$ to constrain the compression cost to the desired value by construction. We demonstrate that variational training with Mean-KL parameterization converges twice as fast and maintains predictive performance after compression. Furthermore, we show that Mean-KL leads to more meaningful variational distributions with heavier tails and compressed weight samples which are more robust to pruning.

cs.LG↗

arXiv2023

Estimating optimal PAC-Bayes bounds with Hamiltonian Monte Carlo

An important yet underexplored question in the PAC-Bayes literature is how much tightness we lose by restricting the posterior family to factorized Gaussian distributions when optimizing a PAC-Bayes bound. We investigate this issue by estimating data-independent PAC-Bayes bounds using the optimal posteriors, comparing them to bounds obtained using MFVI. Concretely, we (1) sample from the optimal Gibbs posterior using Hamiltonian Monte Carlo, (2) estimate its KL divergence from the prior with thermodynamic integration, and (3) propose three methods to obtain high-probability bounds under different assumptions. Our experiments on the MNIST dataset reveal significant tightness gaps, as much as 5-6\% in some cases.

stat.ML↗

arXiv2023

Compression with Bayesian Implicit Neural Representations

Many common types of data can be represented as functions that map coordinates to signal values, such as pixel locations to RGB values in the case of an image. Based on this view, data can be compressed by overfitting a compact neural network to its functional representation and then encoding the network weights. However, most current solutions for this are inefficient, as quantization to low-bit precision substantially degrades the reconstruction quality. To address this issue, we propose overfitting variational Bayesian neural networks to the data and compressing an approximate posterior weight sample using relative entropy coding instead of quantizing and entropy coding it. This strategy enables direct optimization of the rate-distortion performance by minimizing the $β$-ELBO, and target different rate-distortion trade-offs for a given network architecture by adjusting $β$. Moreover, we introduce an iterative algorithm for learning prior weight distributions and employ a progressive refinement process for the variational posterior that significantly enhances performance. Experiments show that our method achieves strong performance on image and audio compression while retaining simplicity.

cs.LG↗

arXiv2023

Faster Relative Entropy Coding with Greedy Rejection Coding

Relative entropy coding (REC) algorithms encode a sample from a target distribution $Q$ using a proposal distribution $P$ using as few bits as possible. Unlike entropy coding, REC does not assume discrete distributions or require quantisation. As such, it can be naturally integrated into communication pipelines such as learnt compression and differentially private federated learning. Unfortunately, despite their practical benefits, REC algorithms have not seen widespread application, due to their prohibitively slow runtimes or restrictive assumptions. In this paper, we make progress towards addressing these issues. We introduce Greedy Rejection Coding (GRC), which generalises the rejection based-algorithm of Harsha et al. (2007) to arbitrary probability spaces and partitioning schemes. We first show that GRC terminates almost surely and returns unbiased samples from $Q$, after which we focus on two of its variants: GRCS and GRCD. We show that for continuous $Q$ and $P$ over $\mathbb{R}$ with unimodal density ratio $dQ/dP$, the expected runtime of GRCS is upper bounded by $βD_{KL}[Q || P] + O(1)$ where $β\approx 4.82$, and its expected codelength is optimal. This makes GRCS the first REC algorithm with guaranteed optimal runtime for this class of distributions, up to the multiplicative constant $β$. This significantly improves upon the previous state-of-the-art method, A* coding (Flamich et al., 2022). Under the same assumptions, we experimentally observe and conjecture that the expected runtime and codelength of GRCD are upper bounded by $D_{KL}[Q || P] + O(1)$. Finally, we evaluate GRC in a variational autoencoder-based compression pipeline on MNIST, and show that a modified ELBO and an index-compression method can further improve compression efficiency.

cs.IT↗